Inorganic Chemistry COSTRIBUTION FROM THE DEPARTMEST OF CHEMISTRY, HARVARD UNIVERSITY, CAMBRIDGE, MASSACHUSETTS 02138
Crystal and Molecular Structure of (CH3),B5H7 BY LAWREKCE B. FRIEDMAN
AND
WILLIAM
N.LIPSCOMB
Received M u y 18, 1966 The apex-.basal dimethylpentaborane, 1,2-(CH3)2B6H,, is shown by X-ray diffraction methods t o rearrange t o the cis basal-basal product, 2,3-(CHs)yBjH7,in which the methyl groups are 011 adjacent basal B atoms of the square-pyramidal Bs unit. Absence of the 2,4 isomer is attributed t o H(methy1). . . H(bridge) repulsions in a proposed trigonal bipyramidal intermediate. The space group is Pmcn, and there are four molecules in the unit cell having parameters a = 12.55, b = 6.39, and is 0.11 for the 343 observed reflections. c = 9.10 9. The value of R = L.I’F,l - ~F,II/ZIF,~
Base-catalyzed rearrangements of pentaborane(9) derivatives proceed a t lower temperatures than do uncatalyzed thermal rearrangements. At room temperature 2,6-dimethylpyridine catalyzes the complete conversion1 of I-CHsBSHg to 2-CH3BjHs. The conversion of B1OH16, which is a BjHg dimer, to a B10H14 derivative also occurszin the presence of 2,6-dimethylpyridine. Plausible internal rearrangement mechani~rnsl-~ facilitated by H tautomerism mere proposed; but the possibility of a mechanism in which the base cleaved5 a BH3 unit which later recombined was not eliminated a t these low temperatures until the isolation6of the (CH3)3T\”+.BsH,C2H6- intermediate and the study7 of the l-DBSHsrearrangement in which a BjHg complex with Lewis base was suggested. Later studies have included rearrangements of monohalogenated derivatives of B6H9catalyzed by A1C138and hexamethylenetetramine. Thermal rearrangements of 1-RBjHe to 2-RBsHs, where R is CH3 or CzHj, occur10 a t 200”. About 80% rearrangement of 1-DBjH8 to 2-DBbHs is found7 in 20 hr a t 145”, but there is little evidence that this intramolecular rearrangement takes place a t a lower temperature than intermolecular H atom exchange,ll which complicates the question of the nature of the intermediate steps. Nevertheless, the preference of a substituent which is more electron donating than H for the basal position is consistent with the predictions of molecular orbital s t ~ d i e swhich ~ j ~ ~indicate that the apex B atom is more negative than the basal B atoms. The base-catalyzed and thermal rearrangements of 1,2-(CH3)2B6H7 might then be expected to yield a mixture of 2,3-(CH3)2BsH7(cis) and 2,4-(CH3)zBgH7(trans) isomers. Surprisingly, however, in the 2,B-dimethylpyridine-catalyzed reaction only a single product was obtained. We show here by single crystal X-ray dif(1) T. P. Onak, J . Am. Chem. Soc., 83, 2584 (1961). ( 2 ) R. N. Grimes and W.K.Lipscomb, Puoc. Xa22. Acad. Sci. U . S., 48, 496 (1962). (3) R. E. Williams, J . I n o u g . Nucl. Chem., 20, 198 (1961). (4) W. N. Lipscomb, “Boron Hydrides,” The W. A. Benjamin Company, New York, N. Y . , 1963. (5) R. W. Parry and L. J. Edwards, J . A m . Chem. S o c . , 81, 3554 (1959). (6) W. V. Hough, L. J. Edwards, and A. F. Stang, ibid., 86, 831 (1963). (7) T. P. Onak, F. J. Gerhart, and R. E. Williams, i b i d . , 86, 1754 (1963). (8) T. P. Onak and G. B. Dunks, I n o u g . Chem., 3, 1060 (1964). (9) A. B. Burg and J. S. Sandhu, J . A m . Chem. SOL.,87, 3787 (1965). (10) T. P. Onak and F. J. Gerhart, Inoug. Chem., 1, 742 (1962). (11) I. Shapiro and B. Keilin, J . A m . Che7n. SOL.,77, 2663 (1955). (12) R . Hoffmann and W. N. Lipsromh, J . C ~ P ~ Phys., N . 87, 2872 (1962).
fraction methods that it is the cis product,132,3-(CH&BjH7. Examination of bond distances and unpublished molecular orbital results indicates no significant thermodynamic difference between these two possible products, and we therefore have searched for a mechanistic interpretation, which may have wider application in the study of rearrangement paths in other polyhedral or near-polyhedral molecular species. Structure Determination The liquid sample of (CH3)2BjH7 was distilled14 and then fractionated into Pyrex capillaries 0.5 mm in diameter. After sealing, these capillaries were mounted on a Weissenberg or precession goniometer and were cooled15to -50’ by means of a cold stream of N2 which was obtained by evaporation of liquid N2. After careful growth of a single crystal, a sample was maintained on a Weissenberg goniometer for some 2 months, during the recording of photographic X-ray (CU K a ) diffraction 8. A second crystal data of levels hkL for 0 6 L mounted on a precession goniometer and photographed with the use of Cu K a radiation yielded levels h01 and OkZ, before the “Great Blackout” (New York Times, Nov 10-15, 1965) terminated the experiment. Although the films covered 74% of the Cu K a sphere of reflection, only 343 diffraction maxima were observed while 301 reflections were classified as below the observational limit. Reciprocal lattice symmetry of Dzh and systematic k odd and of h01 for 1 odd suggest absences of hk0 for h that the orthorhombic space group is either CzV9P21cn or DzhlG-Pmcn. Later work proved that the space group Pmcn, in which the molecule lies on a mirror plane, is the correct choice. Unit cell dimensions of a = 12.55 f 0.04, b = 6.39 f 0.01, and c = 9.10 =t0.04. A were obtained from photographs which had been calibrated with a diffraction pattern of powdered AI. Assumption of four molecules in the unit cell yields a calculated density of 0.830 g ~ m - which ~ , is in reasonable agreement with that expected from a related compound, BjHg,for which the density is160.761 g cm+.
O ; OJ 2y ‘/2; l / z ; ‘/2, ‘/a, 22 ‘/2; and the centrosymmetric interaction, 2x, 2y, 22. Our initial assumption of the space group, Pmcn, proved to be satisfactory : we found eight mutually consistent peaks, which were then carefully examined, taking into account all equivalent positions and symmetry ambiguities, for possible square-pyramidal BE arrangements. After a few false starts, an arrangement with apex B on the crystallographic mirror plane was found and was then shown to be consistent with those peaks sufficiently near the origin that they must necessarily be intramolecular vectors. Further examination then led to all B and C positions. The value of R F = z l l ~ F o-~ lFcl I/ZiFol = 0.44 for this unrefined structure decreased to 0.27 after three cycles in which isotropic thermal parameters and distances were refined. Anisotropic thermal parameters then led to R = 0.22, including all reflections, observed and also absent, a t one-half of each limit of observation. For observed reflections only the value of R was 0.18 a t this stage. Hydrogen atoms were located from difference electron density maps from which B and C were subtracted. The first map contained five largest peaks, from 673 down to 471 in arbitrary units, a t the five H positions of the B5H7 half-molecular unit, of which three were on the crystallographic mirror plane and two were not. Of the remaining seven peaks in the asymmetric unit of this map, three were residuals a t B or C, three a t 400, 386, and 268 were a t about tetrahedral angles around the C atom, and one a t 274 was half-way between two bonded B atoms (less than 1 A from each) and thus deemed to be false. When the eight H atoms of the asymmetric unit were included as fixed atom contributions we obtained a value of R = 0.133 which led finally to a value of R = 0.109 for the 343 observed reflections after refinements of all position parameters for three cycles, of anisotropic thermal parameters of B and C for three cycles, 3f isotropic thermal parameters for H atoms for three cycles, and of scale factors for individual levels of the Weissenberg data for three cycles. Although the isotropic thermal parameters for H were converted to anisotropic equivalents, they were not further refined. Observed structure factors and refined scale factors are listed in Table I. It has, of course, been uniformly17realized for some time that
+
+
+
+
(CH3)2BbH, 1753
+
‘ / z j
(17) E C . Lingafelter and J. Donohue, Acta Curst., 20, 321 (1966).
StALE
L=o L-1 L-2 L.3 L-4 LQ5 L.6 La7 L.8
FACTOR5 6.8705 0.8810 0.9689 0.9715
0.9145 1.0152 1.0543 1.0573 0.8007
a The value of k and the range of h are given in parentheses. Absent reflections are indicated by an asterisk, experimentally unobserved reflections by U, and systematic extinctions by an extra comma. For observed reflections the value of 101F,I and the standard error of IF,/ are listed separated by a slant line. The standard error of IF,] is obtained from the standard error of / F O l 2by
F(O,O,O) is given as a reference point and is summed over the entire unit cell.
one cannot simultaneously refine scale factors about a single axis and those thermal parameters which interact with these scale factors.
1754 LAWRENCE B. FRIEDMAN AND WILLIAM N. LIPSCOMB
Inorganic Chemistry TABLE I1 FISALATOMICPARAMETERS
0
IF
\
0
0.54
vRF2 = 0.95
Atomic Positions in Fractions of the Unit Cell Edge
\
/
\
30 0
\
/
p' / I
2
/
i' i'
k
Y
0.2500 0.1775 0.1784 0.0881 0.2500 0.1185 0.2500 0.1456 0.2500 0.1093 0.0363 0.0714
0,5689 0.5228 0.7729 0.3611 0.0062 0.6419 0,9109 0.7341 0.5318 0.1956 0.3694 0.3745
2
0.0047 0.1538 0.0627 0.1960 0.4108 0.4993 0.1355 0.1944 0.2638 0.1370 0.1111 0.3080
Temperature Factors (A-lnisotropic5X 104) p.1
42 30 45 40 62 50 54 0 13 120 66 104
180
-
2
3
4
__
,
1
,R ,,
0.75
5
E Figure 1.-Variation of the weighted sum of squares of residuals, Zw(iFo! - iFc1)2, denoted by 2 , and agreement factors Rs and w R p , for different choices of (iFoi), The minimum value in the sum of squares of residuals curve occurs a t ( ~ F , ~=) 3.75, which is 47y0 of the lowest readable value before the application of Lorcntz and polarization factors.
p33
p22
209 194 223 274 239 193 207 0 50 462 256 400
013
812
0 14 10 -39
202 216 216 271 118 95 102 0
0 3 -8 -5
023
2'0
-35 -17 0 5 3.89 3.15 3.38 0 0.81 7.54 4.18 6.54
25 228 126 197
Maximum Value of v for Atomic Positions in Fractions of the Unit Cell Edge Atom type
X
Y
2
0.0005 0,0004 0.0088 0,0034
0.0015 0.0009 0.0171 0.0142
0 . 0012 0 . 0010 0 . 0102 0 . 0085
Absent reflections are frequently omitted in refinements or are assigned one-half of the maximum observable in the appropriate region of the film. Neither of these procedures seems as satisfactory as either assigning an average value based upon the corresponding calculated structure factor or assigning an average value by minimizing the weighted sum of squares of residuals, Zw([Fol for different choices of (lFol) for these absent reflections (or similarly for IFI2 in place of IF1 if w is suitably modified). A test of this last procedure yielded a value of (F,) = 3.75, which is 47% of the lowest readable value before the application of Lorentz and polarization factors. When the 301 reflections were included according to this prescription the final value of RF was 0.195 for all observed and absent reflections. Figure 1 shows the weighted sum of squares of residuals and both weighted and unweighted agreement factors, all for absent reflections only, as functions of (Fo).
7 15 B 5 27 8 c 1 13 C 3 17 7 a The thermal parameters are in the form exp -(h2&, k2pzz Pp,, 2hkpla 2hZPI3 2 k l P ~ ) . For atom H(8) the determinant of the matrix of temperature factor components became negative, and hence all values of the temperature factors were reset to zero. the isotropic temperature factor coefficients for the H atoms ( T )were converted to anisotropic equivalents but were not further refined. The x parameters of B ( l ) , H(1'), H(7), and H(9) and the and PI; of B(1) are all rcstrained by symmetry and their standard deviations arc zero. Equivalent positions for space group Pmcn are: x, y,t; 2 , T,Z; x , '/2 31, '/2 - 2; '/2 x, '/2 - x, '/z - y , 1 1 2 2; L / a y , ' / z - 2 ; x , 1/2 - ?, ' / z 2. - x, )I, 2; 52, ' / 2 p, I;
Discussion Final parameters, based upon the 343 observed reflections, are given in Table 11, disagreement factors are listed in Table 111, and bond distances with their standard deviations computed from the full variancecovariance matrix are presented in Table IV. Corrections (Table IV) for thermal motion based upon the assumption that the second atom rides on the first are probably larger than those which mould be obtained from motion of a rigid molecule, but our data do not justify such an exacting treatment. Bond angle standard deviations were calculated using the full variance-
covariance matrix, but those listed in Table V are the maximum values for each type of bond angle in the expectation that the errors are not truly random. The molecule is shown in Figure 2, and the crystal structure in Figure 3 In the molecule (Figure 2 ) the methyl groups are attached to adjacent basal B atoms which are 1.82 A apart, as compared with the three other B(basa1)R(basa1) distances of 1.80 PI. Thus there is no indication that the CH3B-BCH3 bond is abnormally strong compared with the HB-BH bonds of the molecule, or
B
C
H(terminal ) H(bridge)
Maximum Value of
CT
for Temperature Factors
Atom type
+
811
+-
pi2
+
+
012
p13
(3?d
+
+
+
+
+
-+
+
CRYSTAL AND MOLECULAR STRUCTURE OF (CH3)2B5H7 1755
Vol. 5, No. 10,October 1966
TABLE V BONDANGELES
TABLE I11 DISAGREEMENT FACTORB BASEDO N F Sin 0 R 0.00-0.40 0.11 0.40-0.50 0.10 0.50-0.60 0.08 0.60-0.65 0.08 0.6S0.70 0.12 0.70-0.75 0.14 0.75-0.80 0.12 0.80-0.85 0.15 0.17 0.85-0.90 0.90-1.00 0.15 Class
All H = 2N H = 2 N + 1 K = 2N K = 2 N + 1 L = 2N L = 2 N + 1 K + L = 2 N K + L = 2N L + H = 2 N L H = 2N H+K=2N H K = 2N
+1 +1 +1
+ + H + K + L = 2N
HKL
OKL
0.11 0.11 0.11 0.12 0.10 0.11 0.11 0.10 0.12 0.11 0.11 0.12 0.10 0.10
0.10 0.08 0 . 2 0 0.10 0.11 0.08 0.09 0.10 0.11 0.11 0.20 0.17 0.10 0.14 0.10 0.15 0.14 0.14 0.10 0.09 0.10 0.14
HOL
HKO
Atoms
HOO
OK0
0.10
B(4)-B(5)-B(2) B( 3)-B(2)-B( 5) B(2)-B( 1)-B(5) B(2)-B(l)-B(3) B(5)-B(l)-B(4) B( l)-B(5)-H(5) B( 1)-B(2)-C(2/) B(2)-C(2')-H( 10) B( 2)-C(2')-H( 11) B(2)-C(2')-H( 12) H( 10)-C(2')-H( 12) H(lO)-C(B')-H( 11) H( ll)-C(2')-H( 12) L B(1)B(2)B(5)-B(5)B(2)H(8)a L B(1)B(2)B(3)-B(2)B(3)H(9)a L B( l)B(4)B(5)-B(4)B(5)H(7)"
Degrees
C
90.4 89.6 64.5 66.5 65.2 126.3 135.0 107.9 103.8 109.2 123.1 81.3 127.7 203 196 194
0.5 0.5 1.0 1.0 1.0 3.0 1.0 5.0 5.0 5.0 7.0 7.0 7.0 3.0 3.0 3.0
External dihedral angle.
H+K+L= 2N
a
+1
0.11
RF = Z / l F o / - Fat /ZiFol = 0.109 Rpz = Z1F02 - Fo2 / 2 F 0 2 = 0.198 Rwpz = [ZwIFo2 - Fc212/Z~Fo4]1'z = 0.241 Based on all observed reflections.
TABLEI V BONDDISTANCES'
AND STANDARD
Uncorrected
Figure 2.-The
DEVIATIONS IN A
Correctedb
&
B(4)-B(5) 1.80 1.80 0.01 B(2)-B(5) 1.80 1.80 0.01 B(2)-B(3) 1.82 1.82 0.01 B( 11-w5) 1.67 1.67 0.01 B(l)-B(2) 1.66 1.66 0.01 B(2)-C(2') 1.57 1.55 0.01 B( 1)-H( 1') 0.98 0.98 0.09 B(5)-H(5') 1.09 1.11 0.06 B( 5)-W 7 ) 1.42 1.44 0.07 B( 2 )-H( 9 1 1.35 1.38 0.05 J3(5)-H(8) 1.29 1.32 0.04 B(2)-H(8) 1.46 1.50 0.04 C(2')-H( 10) 1.22 1.19 0.09 C(2')-H( 11) 1.01 1.02 0.08 C(2')-H( 12) 1.04 1.01 0.09 a Shortest intermolecular distances: B-B, 3.94; B-C, 4.04; C-C, 4.01; B-H, 3.13; C-H, 3.21; H-H, 2.87. b T h e first The errors listed atom is assumed to be riding on the second. were obtained from the full variance-covariance matrix calculated during the final least-squares refinement of all position parameters and B and C temperature factors.
compared with a similar distancel5v1*of 1.80 A in BjH9. Moreover, the B (basal)-B (apex) distances and the B (basal)-CH~ distances are normal. The B(apex)B(basal)-CH3 angle of 135" in 2,3-(CH3)2BhH7 is in excellent agreement with the microwave valuelB of 136.2" in BSHQand in reasonable agreement, within the
molecular structure and numbering scheme for BF"( CH3)2.
large errors listed, with X-rayL6and electron diffractionLgstudies. Although the B (basal)-C-H angles are close to tetrahedral values, the deviations of HCH angles from 109.5' are perhaps consistent with apparent errors associated with some torsional motion of the CH3 group about the B-C axis. Nevertheless, the H(methy1) atoms are staggered with respect to the H(bridge) atoms. The external dihedral angles of 194, 196, and 203" in (CH3)zBbHy are to be compared with the microwave valuel8 of 196 f 2" in B ~ H Q . Perhaps the somewhat larger value of 203' is associated with the steric interactions which also prevent free rotation of the methyl group. As usual4 all bonded distances to H are too short by about 0.1 A, but there is some uncertainty in the exact location of the H atoms as indicated by their large standard deviations. We first discuss these steric interactions on the assumption that all H atoms remain in the molecule during rearrangement. These steric interactions may play a determinative role in the rearrangement of 1,2-(CH3)2BbH7to 2,3(CH3)2B&H7. If no such special features are present, the previous proposal^^-^ would predict a ratio of two parts of the 2,3 isomer (cis) to one part of the 2,4 iso(19) K. Hedberg, M. E. Jones and V. Schomaker, Pvoc. Natl. Acad. Sei.
(18) H. J. Hrostowski and I but a detailed structural study is needed. Acknowledgment.-We wish to thank the Office of Naval Research, the Advanced Research Projects Agency, and the U. S.Army Research Office for financial support. We are also indebted to Professor Thomas Onak for the sample. (21) R. N. Grimes, J. A m . Chenz. Soc., 88, 1070 (1966). ( 2 2 ) R. Hoffmann and W. N. Lipscomb, J . Chem. Phys., 86, 3489 (1962).
